chapter twelve: decision analysis - university of texas at...
TRANSCRIPT
170
PROBLEM SUMMARY
1. Decision-making criteria without probabilities
2. Decision-making criteria without probabilities
3. Decision-making criteria without probabilities
4. Decision-making criteria without probabilities
5. Decision-making criteria without probabilities
6. Decision-making criteria without probabilities
7. Decision-making criteria without probabilities
8. Decision-making criteria without probabilities
9. Decision-making criteria without probabilities
10. Decision-making criteria without probabilities
11. Decision-making criteria without probabilities
12. Decision-making criteria without probabilities
13. Decision-making criteria without probabilities
14. Decision-making criteria without probabilities
15. Expected value
16. Expected value and opportunity loss
17. Expected value
18. Expected value and opportunity loss, EVPI
19. Expected value
20. Indifferent probability
21. Expected value (12–10)
22. Expected value (12–11 )
23. Expected value, EVPI (12–12)
24. Expected value, EVPI (12–13)
25. Expected value (12–10)
26. Payoff table, expected value
27. Payoff table, expected value
28. Payoff table, expected value
29. Payoff table, expected value
30. Payoff table, decision making withoutprobabilities
31. Expected value (12–14)
32. Decision tree (12–25)
33. Sequential decision tree
34. Sequential decision tree
35. Sequential decision tree
36. Bayesian analysis, EVSI (12–13)
37. Bayesian analysis, EVSI (12–18)
38. Bayesian analysis, EVSI (12–25)
39. Bayesian analysis
40. Sequential decision tree
41. Sequential decision tree
42. Sequential decision tree
43. Sequential decision tree
44. Sequential decision tree
45. EVSI, EVPI (12–44)
46. Sequential decision tree
47. Sequential decision tree
48. Sequential decision tree (12–40)
49. Sequential decision tree (12–14)
50. Bayesian analysis, EVSI
51. Utility
52. Expected value, utility
PROBLEM SOLUTIONS
1. a) Lease land; maximum payoff = $90,000
b) Savings certificate; maximum of minimumpayoffs = $10,000
2. a) Drive-in window; maximum payoff= $20,000
b) Breakfast; maximum of minimum payoffs=$4,000
3. a)
Choose bellhop job.
b) Bellhop: 120,000(.4) + 60,000(.6) = $84,000;management: 85,000(.4) + 85,000(.6) =$85,000; select management job.
c) Bellhop: 120,000(.5) + 60,000(.5) = $90,000;management: 85,000(.5) + 85,000(.5) = 85,000;select bellhop job.
4. a) Course III, maximax payoff = A
b) Course I, maximin payoff = D
Chapter Twelve: Decision Analysis
5. a) Plant corn; maximax payoff = $35,000
b) Plant soybeans; maximin payoff = $20,000
c)
Plant corn; minimum regret = $12,000
d) Corn: $35,000(.3) + 8,000(.7) = $16,100;peanuts: 18,000(.3) + 12,000(.7) = $13,800;soybeans: 22,000(.3) + 20,000(.7) = $20,600;plant soybeans.
e) Corn: 35,000(.5) + 8,000(.5) = $21,500;peanuts: 18,000(.5) + 12,000(.5) = $15,000;soybeans: 22,000(.5) + 20,000(.5) = $21,000;plant corn.
6. Note that this payoff table is for costs.
a) Product 3, minimin payoff = $3.00
b) Product 3, minimax payoff = $6.50
7. a) Build shopping center; maximax payoff = $105,000
b) Lease equipment; maximin payoff = $40,000
c)
Build shopping center.
d) Houses: $70,000(.2) + 30,000(.8) = $38,000;shopping center: $105,000(.2) + 20,000(.8) =$37,000; lease: $40,000(.2) + 40,000(.8) =$40,000; lease equipment.
e) Houses: 70,000(.5) + 30,000(.5) = $50,000;shopping center: 105,000(.5) + 20,000(.5) =$62,500; lease: 40,000(.5) + 40,000(.5) =$40,000; build shopping center.
8. a) Purchase motel; maximax payoff = $20,000
b) Purchase theater; maximin payoff = $5,000
c)
Select either motel or restaurant (both haveminimum regret values of $14,000).
d)Motel: 20,000(.4)— 8,000(.6) = $3,200; restaurant:8,000(.4) + 2,000(.6) = $4,400; theater:6,000(.4) + 5,000(.6) = $5,400; select theater.
e) Motel: – 8,000(.33) + 15,000(.33) +20,000(.33) = $9,000; restaurant: 2,000(.33) +8,000(.33) + 6,000(.33) = $5,333; theater:6,000(.33) + 6,000(.33) + 5,000(.33) = $5,666;select motel.
9. a) LaPlace criterion:EV(A|A) = 10.2(.33) + 7.3(.33) + 5.4(.33) = 7.6EV(G|GT) = 9.6(.33) + 8.1(.33) + 4.8(.33) = 7.4EV(A|N) = 12.5( 33) + 6.5(.33) + 3.2(.33) = 7.3Select Alabama vs. Auburn.
b) Select Alabama vs. Auburn; maximin payoff= 5.4
c) Select Army vs. Navy; maximax payoff = 12.5
10. a) Risk fund, maximax payoff = $147,000
b) Savings bonds maximin payoff = $30,000
c) Money market: 2(.2) + 3.1(.20) + 4(.2) +4.3(.2) + 5(.2) = 36,000; stock growth: –3(.2) –2(.2) + 2.5(.2) + 4(.2) + 6(.2) = 15,000; bond:6(.2) + 5(.2) + 3(.2) + 3(.2) + 2(.2) = 38,000;government: 4(.2) + 3.6(.2) + 3.2(.2) + 3(.2) +2.8(.2) = 33,200; risk: –9(.2) –4.5(.2) + 1.2(.2)+ 8.3(.2) + 14.7(.2) = 21,400; savings bonds:3(.2) + 3(.2) + 3.2(.2) + 3.4(.2) + 3.5(.2) =32,200; select bond fund.
11.
a) Pass, maximax payoff = 20 yd
b) Either off tackle or option, maximin payoff =–2 yd
c) Off tackle: 3(.2) –2(.2) + 9(.2) + 7(.2) –1(.2) =3.2; option: –1(.2) + 8(.2) –2(.2) + 9(.2) +12(.2) = 5.2; toss sweep: 6(.2) + 16(.2) –5(.2) +3(.2) + 14(.2) = 6.8; draw: –2(.2) + 4(.2) +3(.2) + 10(.2) –3(.2) = 2.4; pass: 8(.2) + 20(.2)+ 12(.2) –7(.2) –8(.2) = 5.0; screen: –5(.2)–2(.2) + 8(.2) + 3(.2) + 16(.2) = 4.0;use toss sweep.
12. a) Minimin:South Korea 15.2China 17.6Taiwan 14.9
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Philippines 13.8Mexico 12.5 ← minimumSelect Mexico
b) Minimax:South Korea 21.7China 19.0 ← minimumTaiwan 19.2Philippines 22.5Mexico 25.0Select China
c) Hurwicz (α = .40):South Korea: 15.2(.40) + 21.7(.60) = 19.10China: 17.6(.40) + 19.0(.60) = 18.44Taiwan: 14.9(.40) + 19.2(.60)
= 17.48 ← minimumPhilippines: 13.8(.40) + 22.5(.60) = 19.02Mexico: 12.5(.40) + 25.0(.60) = 20.0Select Taiwan
d) Equal likelihood:South Korea: 21.7(.33) + 19.1(.33) + 15.2(.33) =
18.48China: 19.0(.33) + 18.5(.33) + 17.6(.33) = 18.18Taiwan: 19.2(.33) + 17.1(.33) + 14.9(.33) =
16.90 ← minimumPhilippines: 22.5(.33) + 16.8(.33) + 13.8(.33) =
17.52Mexico: 25.0(.33) + 21.2(.33) + 12.5(.33) = 19.37Select Taiwan
13. a) Maximax criteria:Office park 4.5 ← maximumOffice building 2.4Warehouse 1.7Shopping center 3.6Condominiums 3.2Select office park
b) Maximin criteria:Office park 0.5Office building 1.5 ← maximumWarehouse 1.0Shopping center 0.7Condominiums 0.6Select office building
c) Equal likelihoodOffice park: 0.5(.33) + 1.7(.33) + 4.5(.33)
= 2.21 ← maximumOffice building: 1.5(.33) + 1.9(.33) + 2.4(.33)
= 1.91Warehouse: 1.7(.33) + 1.4(.33) + 1.0(.33)
= 1.35Shopping center: 0.7(.33) + 2.4(.33) + 3.6(.33)
= 2.21 ← maximumCondominiums: 3.2(.33) + 1.5(.33) + 0.6(.33)
= 1.75
Select office park or shopping center
d) Hurwicz criteria (α = .3)Office park: 4.5(.3) + 0.5(.7) = 1.70 Office building: 2.4(.3) + 1.5(.7) =
1.77 ← maximumWarehouse: 1.7(.3) + 1.0(.7) = 1.21Shopping center: 3.6(.3) + 0.7(.7) = 1.57Condominiums: 3.2(.3) + 0.6(.7) = 1.38Select office building
14. a) Maximax = Gordan
b) Maximin = Johnson
c) Hurwicz (� = .60)
Byrd = 4.4(.6) + (–3.2)(.4) = $1.36MO’Neil = 6.3(.6) + (–5.1)(.4) = $1.74MJohnson = 5.8(.6) + (–2.7)(.4) = $2.40MGordan = 9.6(.6) + (–6.3)(.4) = $3.24MSelect Gordan
d) Equal likelihood
Byrd = 4.4(.33) + (1.3)(.33) + (–3.2)(.33) = +$0.83MO’Neil = 6.3(.33) + (1.8)(.33) + (–5.1)(.33) = +$.99M
Johnson = 5.8(.33) + (0.7)(.33) + (–2.7)(.33) = +$1.254MGordan = 9.6(.33) + (–1.6)(.33) + (–6.3)(.33) = $.561MSelect Johnson
15. EV(press) = 40,000(.4) – 8,000(.6) = $11,200;EV(lathe) = 20,000(.4) + 4,000(.6) = $10,400;EV(grinder) = 12,000(.4) + 10,000(.6)= $10,800; purchase press.
16. a) EV(sunvisors) = –500(.3) –200(.15) +1500(.55) = $645; EV(umbrellas) = 2,000(.3) +0(.15) – 900(.55) = $105; carry sunvisors.
b) Opportunity loss table:
EOL(sunvisors) = 2,500(.3) + 200(.15) + 0 =$780; EOL(umbrellas) = 0 + 0 + 2,400(.55) =$1,320; select sunvisors since it has theminimum expected regret.
17. EV (snow shoveler) = $30(.13) + 60(.18) +90(.26) + 120(.23) + 150(.10) + 180(.07) +210(.03) = $99.60
The cost of the snow blower ($625) is muchmore than the annual cost of the snow shoveler,thus on the basis of one year the snow shovelershould be used. However, the snow blowercould be used for an extended period of timesuch that after approximately six years the costof the snow blower would be recouped. Thus,the decision hinges on weather or not the
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decision maker thinks 6 years is too long towait to recoup the cost of the snow blower.
18. a) EV(widget) = 120,000(.2) + 70,000(.7)–30,000(.1) = $70,000; EV(hummer) =60,000(.2) + 40,000(.7) + 20,000(.1) =$42,000; EV(nimnot) = 35,000(.2) + 30,000(.7)+ 30,000(.1) = $31,000; introduce widget.
b)
EOL(A) = 0 + 0 + 60,000(.1) = $6,000;EOL(B) = 60,000(.2) + 30,000(.7) + 10,000(.1)= $34,000; EOL(C) = 85,000(.2) + 40,000(.7)+ 0 = $45,000; select A (widget).
c) Expected value given perfect information =120,000(.2) + 70,000(.7) + 30,00()(.1) =76,000; EVPI = 76,000— EV(widget) =76,000—70,000 = $6,000; the company wouldconsider this a maximum, and since perfectinformation is rare, it would pay less than$6,000 probably.
19. EV(operate) = 120,000(.4) + 40,000(.2) +(–40,000)(.4) = $40,000; leasing = $40,000; ifconservative, the firm should lease. Althoughthe expected value for operating is the same asleasing, the lease agreement is not subject touncertainty and thus does not contain thepotential $40,000 loss. However, the risk takermight attempt the $120,000 gain.
20. To be indifferent, the expected value for theinvestments would equal each other: EV(stocks)= EV(bonds). Next, let the probability of goodeconomic conditions equal p and the probabilityof bad conditions equal 1 – p:
EV(stocks) = 10,000( p) + –4,000(1 – p)
EV(bonds) = 7,000(p) + 2,000(1 – p)
EV(stocks) = EV(bonds)10,000(p) + (-4,000) (1 – p) = 7,000(p) +
2,000(1 – p)10,000p – 4,000 + 4,000p = 7,000p + 2,000
– 2,000p9,000p = 6,000
p = .667Therefore, probability of good conditions =p =.667, probability of bad conditions = 1 – p= .333.
21. EV(money market) = 2(.2) + 3.1(.3) + 4(.3) +4.3(.1) + 5(.1) = 34,600; EV(stock growth) =–3(.2) – 2(.3) + 2.5(.3) + 4(.1) + 6(.1) = 5,500:EV(bond) = 6(.2) + 5(.3) + 3(.3) + 3(.1) + 2(.1)= 41,000; EV(government) = 4(.2) + 3.6(.3)3.2(.3) + 3(.1) + 2.8(.1) = 34,200; EV(risk) =–9(.2) – 4.5(.3) + 1.2(.3) + 8.3(.1) + 14.7(.1) =–49,000; EV(savings bonds) = 3(.2) + 3(.3)3.2(.3) + 3.4(.1) + 3.5(.1) = 31,500; purchasebond fund.
22. a) EV(off tackle) = 3(.4) – 2(.10) + 9(.20) +7(.20) – 1(. 10) = 4.10; EV(option) = -1(.4) +8(.10) – 2(.20) + 9(.2) + 12(.10) = 3; EV(tosssweep) = 6(.4) + 16(.10) – 5(.20) + 3(.20) +14(.10) = 5.0; EV(draw) = – 2(.4) + 4(.10) +3(.20) + 10(.20) - 3(.10) = 1.9; EV(pass) = 8(.4)+ 20(.10) + 12(.20) – 7(.20) – 8(.10) = 5.4;EV(screen) = – 5(.4) – 2(.10) + 8(.20) + 3(.20)+ 16(.10) = 1.6; PASS is best, followed by tosssweep, off tackle, option, draw, and screen.
b) EV(off tackle) = 3(.10) – 2(.10) + 9(.10) +7(.10) – 1(.60) = 1.1; EV(option)= –1(.10) +8(.10) – 2(.10) + 9(.10) + 12(.60) = 8.6;EV(toss sweep) = 6(.10) + 16(.10) – 5(.10) +3(.10) + 14(.60) = 10.4; EV(draw) = – 2(.10) +4(.10) + 3(.10) + 10(.10) – 3(.60) = –.3;EV(pass) = 8(.10) + 20(.10) + 12(.10) – 7(.10)– 8(.60) = –1.5; EV(screen) = – 5(.10) – 2(.10)+ 8(.10) + 3(.10) + 16(.60) = 10.0; select tosssweep. Yes, it is likely Tech will make the firstdown.
23. EV (South Korea) = 21.7(.40) + 19.1(0.5) + 15.2(.10) =19.75
EV (China) = 19.0(.40) + 18.5(.50) + 17.6(.10) = 18.61
EV (Taiwan) = 19.2(.40) + 17.1(.50) + 14.9(.10) = 17.72 ← minimum
EV (Philippines) = 22.5(.40) + 16.8(.50) + 13.8(.10) = 18.78
EV (Mexico) = 25.0(.40) + 21.2(.50) + 12.5(.10) = 21.85
Select TaiwanExpected value of perfect information =19(.40) + 16.8(.50) + 12.5(.10) = 17.25EVPI = 17.25 – 17.72= $-0.47 million
The EVPI is the maximum amount the cost ofthe facility could be reduced ($0.47 million) ifperfect information can be obtained.
24. a) EV (Office park) = .5(.50) + 1.7(.40) + 4.5(.10) = 1.38
EV (Office building) = 1.5(.50) + 1.9(.40) + 2.4(.10) = 1.75
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EV (Warehouse) = 1.7(.50) + 1.4(.40) + 1.0(.10) = 1.51
EV (Shopping center) = 0.7(.50) + 2.4(.40) + 3.6(.10) = 1.67
EV (Condominiums) = 3.2(.50) + 1.5(.40) + .06(.10) = 2.26 ← maximum
Select Condominium project
b) EVPI = Expected value of perfect information– expected value without perfect information =3.01 – 2.26EVPI = $0.75 million
25. Using expected value; EV(compacts) =300,000(.6) + 150,000(.4) = $240,000; EV(full-sized) = –100,000(.6) + 600,000(.4) =$180,000; EV(trucks) = 120,000(.6) +170,000(.4) = $140,000; select the compact cardealership.
26. Payoff matrix:
EV(20) = $20.00/; EV(21) = 18.50(.1) +21.00(.2) + 21.00(.3) + 21.00(.3) + 21.00(.1) =$20.75; EV(22) = 17.00(.1) + 19.50(.2) +22.00(.3) + 22.00(.3) + 22.00(.1) = $21.00;EV(23) = 15.50(.1) + 18.00(.2) + 20.50(.3) +23.00(.3) + 23.00(.1) = $20.50; EV(24) =14.00(.1) + 16.50(.2) + 19.00(.3) + 21.50(.3) +24.00(.1) = $19.25; stock 22 lb.
27. Revenue and cost data: sales revenue =$12.00/case; cost = $10/case; salvage forunsold cases = $2/case; shortage cost = $4/case
a) Payoff matrix:
b) EV(15) = 30(.2) + 26(.25) + 22(.4) + 18(.15) =$24.00; EV(16) = 22(.2) + 32(.25) + 28(.4) +24(.15) = $27.20; EV(17) = 14(.2) + 24(.25) +34(.4) + 30(.15) = $26.90; EV(18) = 6(.2) +16(.25) + 26(.4) + 36(.15) = $21.00; stock 16cases.
c) Opportunity loss table:
EOL(15) = 0(.2) + 6(.25) + 12(.4) + 18(.15) =$9.00; EOL(16) = 8(.2) + 0(.25) + 6(.4) +12(.15) = $5.80; EOL(17) = 16(.2) + 8(.25) +0(.4) + 6(.15) = $6.10; EOL(18) = 24(.2) +16(.25) + 8(.4) + 0(.15) = $12.00; stock 16cases.
d) Expected value with perfect information =$30(.2) + 32(.25) + 34(.4) + 36(.15) = $33;EVPI = 33 – EV(16) = 33 – 27.20 = $5.80
28. a) Payoff matrix:
b) EV(25) = 50(.10) + 50(.15) + 50(.30) + 50(.20)+ 50(.15) + 50(.10) = 50.0; EV(26) = 49(.10) +52(.15) + 52(.30) + 52(.20) + 52(.15) + 52(.10)= 51.7; EV(27) = 48(.10) + 51(.15) + 54(.30) +54(.20) + 54(.15) + 54(.10) = 52.95; EV(28) =47(.10) + 50(.15) + 53(.30) + 56(.20) + 56(.15)+ 56(.10) = 53.3; EV(29) = 46(.10) + 49(.15) +52(.30) + 55(.20) + 58(.15) + 58(.10) = 53.05;EV(30) = 45(.10) + 48(.15) + 51(.30) + 54(.20)+ 57(.15) + 60(.10) = 52.35; since EV(28) =$53.30 is the maximum, 28 boxes of Christmascards should be stocked.
c) Compute expected value under certainty: EV=50(.10) + 52(.15) + 54(.30) + 56(.20) + 58(.15)+ 60(.10) = $54.90; EVPI = $54.90 – $53.30 =$1.60
29. a) Payoff matrix:
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b) EV(20) = 20.00(.05) + 18.00(.10) + 16.00(.25)+ 14.00(.30) + 12.00(.20) + 10.00(.10) =$14.40; EV(22) = 17.50(.05) + 22.00(.10) +20.00(.25) + 18.00(.30) + 16.00(.20) +14.00(.10) = $18.08; EV(24) = 15.00(.05) +19.50(.10) + 24.00(.25) + 22.00(.30) +20.00(.20) + 18.00(.10) = $21.10; EV(26) =12.50(.05) + 17.00(.10) + 21.50(.25) +26.00(.30) + 24.00(.20) + 22.00(.10) = $22.50;EV(28)= 10.00(.05) + 14.50(.10) + 19.00(.25)+ 23.50(.30) + 28.00(.20) + 26.00(.10) =$21.95; EV(30) = 7.50(.05) + 12.00(.10) +16.50(.25) + 21.00(.30) + 25.50(.20) +30.00(.10) = $20.10; since EV(26) = $22.50 isthe maximum, the green house owner shouldgrow 26 dozen carnations.
c) Opportunity cost table:
EOL(20) = 0(.05) + 4.00(.10) + 8.00(.25) +12.00(.30) + 16.00(.20) + 20.00(.10) = $11.20;EOL(22) = 2.50(.05) + 0(.10) + 4.00(.25) +8.00(.30) + 12.00(.20) + 16.00(.10) = $7.53;EOL(24) = 5.00(.05) + 2.50(.10) + 0(.25) +4.00(.30) + 8.00(.20) + 12.00(.10) = $4.50;EOL(26) = 7.50(.05) + 5.00(.10) + 2.50(.25) +0(.30) + 4.00(.20) + 8.00(.10) = $3.10;EOL(28) = 10.00(.05) + 7.50(.10) + 5.00(.25) +2.50(.30) + 0(.20) + 4.00(.10) = $3.65;EOL(30) = 12.50(.05) + 10.00(.10) + 7.50(.25)+ 5.00(.30) + 2.50(.20) + 0(.10) = $5.50; sinceEOL(26) = $3.10 is the minimum, 26 dozencarnations should be grown.
d) The expected value under certainty: EV =$20.00(.05) + 22.00(.10) + 24.00(.25) +26.00(.30) + 28.00(.20) + 30.00(.10) = $25.60;EVPI = $25.60 – 22.50 = $3.10
30. a) Stock 25, maximum of minimum payoffs = $50
b) Stock 30, maximum of maximum payoffs =$60
c) 25: 50(.4) + 50(.6) = 50; 26: 52(.4) + 49(.6) =50.2; 27: 54(.4) + 48(.6) = 50.4; 28: 56(.4) +47(.6) = 50.6; 29: 58(.4) + 46(.6) = 50.8; 30:60(.4) + 45(.6) = 51; stock 30 boxes.
d) Stock 28 or 29 boxes; minimum regret = $4.
31. EV(Byrd) = (–3.2)(.15) + (1.3)(.55) +(4.4)(.30) = $1.56M
EV (O’Neil) = (–5.1)(.18) + (1.8)(.26) +(6.3)(.56) = $3.08M
EV (Johnson) = (–2.7)(.21) + (0.7)(.32) +(5.8)(.47) = $2.38M
EV (Gordan) = (–6.3)(.30) + (1.6)(.25) +(9.6)(.45) = $2.03M
Select O’Neil
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32. Select compact car.
33.
34.
NotInstalled
Install
Poweroutage
NoPowerOutage
Largeloss
Slightloss
$495,000
$4,950,000
.10
.90
.05
.95
$80,000,000
$80,000
$1,000,000
$0
Since cost of installation ($800,000) is greaterthan expected value of not installing($495,000), do not install an emergency powergenerator
177
36.
178
37.38.
179
b. Expected value given perfect information =300,000(.6) + 600,00(4) = $420,000; EVPI =$420,000 – 240,000 = $180,000; EVSI =$102,094; efficiency = EVSI/EVPI =$102,094/$180,000 = .51 or 51%
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39. P(s) = .10P(f) = .90G = good review
B = bad review
P(G|s) = .70
P(B|s) = .30
P(G|f) = .20
P(B|f) = .80
P(s|G) =
= = .28
P(f |G) = .72P(s|B) = .04 P(G) = .25P(f |B) = .96 P(B) = .75
(.70)(.10)���(.70)(.10) + (.20)(.90)
P(G|s) P(s)���P(G|s) P(s) + P(G|f) P(f)
1
2
3
4
5
6
7
$0.31M
Good ReviewP(G) = .25
Bad ReviewP(B) = .75
$1.24M
$1.24M
$0
$0
$0
Produce
Don’tProduce
Don’tProduce
Produce
–$6.68M
–$8M
FailureP(f|B) = .96
FailureP(f|G) = .7
$25M
–$8M
$25M
SuccessP(s|B) = .04
SuccessP(s|G) = .28
EVSI = EVwith information – EVw/o information
= $0.31M – (–4.7M)= $5.01M
Hire Sickel; if good review produce, if badreview don’t produce
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3,449,000
Success/win
Fail/lose
.33
.67
$1,700,000
$7,200,000
$7,000,000
$1,700,000
$1,700,000
2,738,800
3,449,000
Success
0.98
0.02
FailTech should go for 2 points
Overtime
Lose
.20
.80
Win
4
2 points
1 point
1
2
3
(b) .98[7.0x + 1.7 (1-x)] + (0.2)(1.7) = 3.449.98[5.3x + 1.7) + .034 = 3.4495.194x + 1.666 + .034 = 3.449
5.194x = 1.749
x = .3367 probability of winning in overtime
40.
(a)
182
587,500
Win
Lesser award0.5
500
Full award
–75,000
$600,000
600,000
Jay should settle
LoseSue
Settle
1
2,000,000
0.5
1,250,000
2
.5
.5
3
0.5
42. The following table includes the medical costs for all thefinal nodes in the decision tree.
Expense Plan 1 Plan 2 Plan 3
100 484 160 388500 884 560 438
1,500 984 1,290 7383,000 1,134 1,440 1,1885,000 1,334 1,640 1,788
10,000 1,834 2,140 3,288
E(1) = 954E(2) = 976.5E(3) = 820.5
Select plan 3
41.
183
36,200
40,300
35,700
39,380
.30.30
.10
.10
Select grower B
2%
8%
6%
4%Grower
B
1
.20
10%33,400
38,000
42,600
3
GrowerA
39,380
40,200
32,200
.15.20
.30
.25
2%
8%
6%
4%
.25
10%28,200
36,200
44,200
2
43.
184
534,000
450,000
Conduct test market
Abandon
GrowerB
–150,000
TestMarket
534,000
Failure
Negative
.20
0.4
0.6
Market
.30
(–150,000)
–$700,000
1,140,000
–150,000
Abandon
5
Positive
4
8
Failure
Success
Success
$1,600,000
–$700,000
$1,600,000
.72
.80
Market990,000
–150,000
Abandon
Market
6
Success
Failure
.50
.50NoTestMarket
2
1
–$700,000
$1,600,000
7
3
45. The EV without the test market is $450,000, which is $84,000 less than the EV wih the test market. Since thecost of the test market is $150,000,
EVSI = $150,000 + 84,000 = $234,000EVPI = $800,000 + 450,000 = $350,000
44.
1,160,00
185
31,780
65,200
210,000
Global
25,000
10,000
265,000
65,000
Reinvest43,000
Internet
1
11
Sell
Up 0.6
Down 0.4(–225,000)
–8,000
–25,000
26,000
Reinvest
Sell
Up 0.6
Down 0.4(–192,000)
226,000175,000
12
–8,000
5
2
5
Up
Down
225,000
0.7
0.3
192,000
(–200,000)
534,000
240,000
35,000
40,000
300,000
100,000
Reinvest76,000
13
Sell
Up 0.6
Down 0.4
(–235,000)
5,000
10,000
60,000
Reinvest
Sell
Up 0.6
Down 0.4(–205,000)
260,000
210,00014
40,000
7
3
8
Up
Down
235,000
0.7
0.3205,000
(–200,000)
56,600
190,000
60,000
–10,000
360,000
160,000
Reinvest92,000
11
Sell
Up 0.6
Down 0.4
(–225,000)
–35,000
–110,000
30,000
Reinvest
Sell
Up
Down 0.4
(+65,000)
230,000
0.6
90,00012
–26,000
9
2
10
Up
Down
260,000
0.7
0.3 165,000
Index
(–200,000)
Ellie should invest in the index fund with an expected return of $65,200.
46.
6
65,200
(�260,000)
15
16
4
186
1
$116
$76.40
$62.80
$120
$710
$50
.10
Defect
Defect
.70
.90
.10
.90
.30Sample negative,
emergency maintenance
.20
.80
Sample positive,unnecessary maintenance
Sample positive,maintenance required
Sample negative
2
6
7No defect
No defect
$1,200
$1,200
$0
$0
$500
$250
9
8
3
11
10
12
13
$48
$710
$50
.04
Defect
Defect
.7
.96
.04
.96
.3Sample negative,
emergency maintenance
.20
.80
Sample positive,unnecessary maintenance
Sample positive,maintenance required
Sample negative,no maintenance
14
15No defect
No defect
$1,200
$1,200
$0
$0
$500
$250
17
16
19
18
20
21
(1) Nomaintenance
($0)
(2) Oilsample($20)
$120$136
(3) Oilchange($14.80)
$111.20
$62.80
(4) Oilchange and
sample($34.80)
4
5
47.
Select strategy 3
187
1
$806
$466.40
$300
$1500
$5,900
$240
.10
Defect
Defect
.70
.90
.10
.90
.30Sample negative,
emergency maintenance
.20
.80
Sample positive,unnecessary maintenance
Sample positive,maintenance required
Sample negative
2
6
7No defect
No defect
$15,000
$15,000
$0
$0
$2,000
$1,200
9
8
3
11
10
12
13
$200
$5,900
$240
.04
Defect
Defect
.7
.96
.04
.96
.3Sample negative,
emergency maintenance
.20
.80
Sample positive,unnecessary maintenance
Sample positive,maintenance required
Sample negative,no maintenance
14
15No defect
No defect
$5,000
$15,000
$0
$0
$2,000
$1,200
17
16
19
18
20
21
(1) Nomaintenance
($0)
(2) Oilsample($30)
$1500$836
(3) Oilchange($100)
$300
(4) Oilchange and
sample($130)
4
5
$596.40
48.